AMPS I · Week 07 — Weak Derivatives and Sobolev Spaces, Céa’s Lemma, Elliptic Regularity, Aubin–Nitsche; Computing Convergence Rates Correctly

File What When
W07_lecture.html (.qmd source) Lecture slides — Parts A, B, C, D in class
W07_lab.ipynb (Colab) In-class lab: regularity decides the rate (interpolating r^\alpha), four ways to compute an error, the L-shaped domain, graded meshes, LLM demo in class (≈ 80 min)
W07_HW7.ipynb (Colab) HW7 — a rate report: proofs (weak derivatives, Aubin–Nitsche, zero error), predicted vs observed rates on a smooth and two corner problems with uniform and graded meshes, measurement pitfalls, LLM claims checked against your numbers due before Week 8
../dolfinx_0.11_api_reference.md DOLFINx 0.11 API reference sheet (§11 parallel-safe norms) — paste it into your LLM always

Open a notebook in Colab: click its link on the course page or below — it opens in Colab; then File → Save a copy in Drive and work on that copy. (Or upload the .ipynb to Google Drive → right-click → Open with → Google Colaboratory.) Run the setup cell first (≈ 3–5 min); re-run it after every runtime restart.

Where code can run: basix, ufl, dolfinx are used only inside %%fenicsx cells. Ordinary cells have NumPy and matplotlib only.

Before submitting: Runtime → Restart session and run all, fill in the AI-usage log, download the .ipynb. An error inside a %%fenicsx cell does not stop Run all: the traceback is printed and the next cell runs anyway. Scroll through every output before you submit. A cell that printed a traceback, and any plot that uses its results, earns no points.

Week 8 starts with the midterm exam (Weeks 1–7, closed-AI, 90 minutes) — there is no separate quiz on this week’s material.